Question

What effective rate of interest is being charged if a golf club's $10,000 initiation fee is paid by 12 beginning-of-month payments of $1000?

(a) 10%
(b) 12%
(c) 15%
(d) 20%

Answer 1

To find the effective rate of interest, calculate the present value of the payments and solve for the interest rate.

Step-by-step explanation:

To find the effective rate of interest being charged, we need to calculate the present value of the initiation fee and then find the interest rate that would equate this present value to the total amount paid.

1. Calculate the present value by summing the present values of each monthly payment. The present value of a payment made at the beginning of the period can be calculated using the formula: PV = PMT * [1 - (1 + r)^(-n)] / r, where PV is the present value, PMT is the monthly payment, r is the interest rate, and n is the number of payments.
2. Set up an equation to find the interest rate. The equation should be: PV = $10,000, which is the initiation fee. Solve this equation for the interest rate r.
3. Convert the interest rate to a percentage to obtain the effective rate of interest charged.

The effective rate of interest being charged is approximately 20% according to the given payment schedule.